Optimization of Network Robustness to Random Breakdowns

TL;DR

This paper identifies an optimal network configuration that maximizes robustness to random node failures, consisting of a mix of high-degree hubs and degree-1 nodes, outperforming scale-free networks.

Contribution

It introduces a novel network design with a specific hub-and-periphery structure that optimizes robustness to random breakdowns for given network size and cost.

Findings

Optimal network has q high-degree hubs and degree-1 nodes.

Robustness fraction f_c approaches 1 as 1/√N.

Outperforms scale-free networks in robustness.

Abstract

We study network configurations that provide optimal robustness to random breakdowns for networks with a given number of nodes $N$ and a given cost--which we take as the average number of connections per node $\kav$. We find that the network design that maximizes $f_c$, the fraction of nodes that are randomly removed before global connectivity is lost, consists of $q=[(\kav-1)/\sqrt\kav]\sqrt N$ high degree nodes (``hubs'') of degree $\sqrt{\kav N}$ and $N-q$ nodes of degree 1. Also, we show that $1-f_c$ approaches 0 as $1/\sqrt N$--faster than any other network configuration including scale-free networks. We offer a simple heuristic argument to explain our results.